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tfg_garriga_puig_jordi.pdf (1.32 MB)

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Bachelor thesis

Publication date

2022-06-13

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cc-by-nc-nd (c) Jordi Garriga Puig, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/189761

Superfı́cies cúbiques i corbes quàrtiques

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Abstract

[en] In Algebraic Geometry numbers 27 and 28 are usually associated with two well-known classical results. All smooth cubic surfaces contain 27 distinct lines. And all smooth plane quartics have 28 bitangents. The aim of this work is to stablish a relation between these two statements. First, we have introduced the theoretical basis needed to demonstrate the two classical results. In the final part, we have suggested a method with which the 27 lines contained in a cubic surface can be transformed into bitangents of a plane quartic and, also from the surface, an additional bitangent can be formed, so that we ultimately obtain the 28 bitangents.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Juan Carlos Naranjo del Val

Subject

Geometria algebraica, Treballs de fi de grau, Corbes algebraiques, Superfícies algebraiques, Superfícies cúbiques, Corbes planes

Subject (English)

Algebraic geometry, Bachelor's theses, Algebraic curves, Algebraic surfaces, Cubic surfaces, Plane curves

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

JORDI, Garriga Puig. Superfı́cies cúbiques i corbes quàrtiques. [consulted: 9 of June of 2026]. Available at: https://hdl.handle.net/2445/189761

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